Answer:
The equation [tex]4\cdot x^{2} + 20\cdot x + 25 = 0[/tex] is equal to [tex]\left(x + \frac{5}{2} \right)^{2} = 0[/tex].
Step-by-step explanation:
Let be the equation [tex]4\cdot x^{2} + 20\cdot x + 25 = 0[/tex], we proceed to rewrite the equation solely by algebraic means:
1) [tex]4\cdot x^{2} + 20\cdot x + 25 = 0[/tex] Given
2) [tex](2\cdot x)^{2} + 10\cdot (2\cdot x) + 25 = 0[/tex] Definition of power/Associative property
3) [tex](2\cdot x + 5)^{2} = 0[/tex] Perfect square trinomial
4) [tex]2^{2}\cdot \left(x + \frac{5}{2} \right)^{2} = 0[/tex] Distributive property/[tex](a\cdot b)^{c} = a^{c}\cdot b^{c}[/tex]
5) [tex]4\cdot (x + \frac{5}{2} )^{2} = 0[/tex] Definition of power
6) [tex]\left(x + \frac{5}{2} \right)^{2} = 0[/tex] Compatibility with multiplication/Commutative and modulative properties/[tex]a\cdot 0 = 0[/tex]
Here are the population figures of five different cities. 371,265 635,155 226,710 468,920 724,435 What is the difference between the largest population and the smallest population?
Answer:
497,725
just subtract smallest from largest to get the difference
724,435 - 226,710
Answer:
largest population 724,435Smallest population 226,710Rivers created a model of her school building. A prism has a length of 5 inches, height of 1 inch, and width of 3 inches. What is the surface area of the model Rivers made? 9 square inches 31 square inches 46 square inches 52 square inchesv
Answer:
46
Step-by-step explanation:
Answer:
c. 46
Step-by-step explanation:
On Edge
Sadie and Connor both play soccer. Connor scored 2 times as many goals as Sadie. Together they scored 9 goals. Could Sadie have scored 4 goals? Why or why not?
Answer:
no
the goal total would be too high
Step-by-step explanation: If Sadie had scored 4 goals, Connor would have scored 2 times 4 = 8 goals. Their goal total would then be 4+8 = 12, not 9. Sadie cannot have scored 4 goals.
__
If we let s represent the number of goals Sadie scored, then 2s is the number Connor scored. Their total is ...
s + 2s = 9
3s = 9 . . . . . . collect terms
s = 9/3 = 3 . . . divide by the coefficient of s
Sadie scored 3 goals. (s=4 is not the solution to the problem)
Rounding in the calculation of monthly interest rates is discouraged. Such rounding can lead to answers different from those presented here. For long-term loans, the differences may be pronounced.
Assume that you take out a $3000 loan for 30 months at 8.5% APR. What is the monthly payment? (Round your answer to the nearest cent.)
Answer:
111.35
Step-by-step explanation:
effective rate: .085/12= .00708333333333
[tex]3000=x\frac{1-(1+.00708333333333)^{-30}}{.00708333333333}\\x=111.35[/tex]
The total cost (in dollars) for a company to manufacture and sell x items per week is C=40x+180, whereas the revenue brought in by selling all x items is R=68x−0.4x2. How many items must be sold to obtain a weekly profit of $300?
Answer:
The company needs to sell either 30 or 40 items.
Step-by-step explanation:
We are given that the cost for selling x items given by the function:
[tex]C(x)=40x+180[/tex]
And the revenue for selling x items is given by:
[tex]R(x)=68x-0.4x^2[/tex]
The profit function is the cost function subtracted from the revenue function:
[tex]P(x)=R(x)-C(x)[/tex]
Substitute and simplify:
[tex]\displaystyle \begin{aligned} P(x)&=(68x-0.4x^2)-(40x+180)\\&=68x-0.4x^2-40x-180\\&=-0.4x^2+28x-180\end{aligned}[/tex]
To find how many items must be sold in order to obtain a weekly profit of $300, we can let P equal 300 and solve for x. So:
[tex]300=-0.4x^2+28x-180[/tex]
Solve for x. Subtract 300 from both sides:
[tex]-0.4x^2+28x-480=0[/tex]
We can divide both sides by -0.4:
[tex]x^2-70x+1200=0[/tex]
Factor:
[tex](x-40)(x-30)=0[/tex]
Zero Product Property:
[tex]x-40=0\text{ or } x-30=0[/tex]
Solve for each case:
[tex]x=40\text{ or } x=30[/tex]
So, in order to obtain a weekly profit of $300, the company need to sell either 30 or 40 items.
Which one of these equations match the graph?
Answer:
C y = 2sin(1/3) x
Step-by-step explanation:
It's a sin function since y = 0 at x = 0
The amplitude is 2
There are 2 cycles in 12π
so the period is 6π
The x coefficent is then 2π/6π = 1/3
Answer
C y = 2sin(1/3) x
Find the value of x . PLEASE ANSWER QUICK ILL MARK BRAINLIEST
Answer:
x = 3
Step-by-step explanation:
both angles together equal 180
Set your formula as
180 = 5x + 165
180 - 165 = 5x
15 = 5x
15/5 = x
3 = x
Answer:
[tex]x[/tex] = 3
Step-by-step explanation:
180° - 165° = 15°
[tex]5x[/tex] = 15
[tex]x[/tex] = 3
Determine the value of x
Answer:
the answer is "C" because I did it on Khan academyThe value of x in the triangle is 17.51
Option C is the correct answer.
We have,
From the figure,
We can use the tangent function.
This means,
Tan = perpendicular / Base
i.e
tan 35 = x / 25
0.700 = x / 25
x = 0.700 x 25
x = 17.5
Thus,
The value of x in the triangle is 17.51.
Learn more about trigonometric identities here:
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URGENT PLEASE ANSWER
Three friends, Cleopatra, Dalila, and ebony fo shopping. The money they have each is in the ratio
Cleopatra : Dalila : Ebony =
5 : 7 : 8
A) How many dollars do they have in total?
B) Dalila spends 12$ on a hat, how many dollars does she have left?
Answer:
A)$60
B)$9
Step-by-step explanation:
THIS IS THE COMPLETE QUESTION BELOW
Three friends, Cleopatra, Dalila, and ebony fo shopping. The money they have each is in the ratio
Cleopatra : Dalila : Ebony =
5 : 7 : 8
Cleopatra has $15.
A) How many dollars do they have in total?
B) Dalila spends 12$ on a hat, how many dollars does she have left?
A)
Total ratio=(5 +7 +8)= 20
Cleopatra has $15.
Let X = total money
Ratio of Cleopatra= 5/20 ×X=15
5X /20 = 15
5X= (15×20)
X= $60
They have $60 in total
B) ratio of Dalila= 7/20 × 60 = $21
But 12$ was spent by Dalila on a hat
Then Dalila will have ($21 - 12$) Left
= $9
PLS HELP ASAP! FIND THE AREA OF THIS FIGURE, THANK YOU!
Answer:
A = [12 + 9(pi)] yd^2 = 40.3 yd^2
Step-by-step explanation:
A = area of triangle + area of semicircle
A = bh/2 + (pi)r^2
A = (6 yd)(4 yd)/2 + (pi)(3 yd)^2
A = 12 yd^2 + 9(pi) yd^2
A = [12 + 9(pi)] yd^2 = 40.3 yd^2
(2104ft)(1 yd/3 ft)(1 football field/100 yds
9514 1404 393
Answer:
7 1/75 football fields
Step-by-step explanation:
Multiply it out. The units of feet and yards cancel, leaving football fields.
= (2104·1·1)/(3·100) football fields ≈ 7.0133... football fields
= 7 1/75 football fields
Consider the dataset below and respond to the questions that follow: Advertisement ($'000) Sales ($'000) 1068 4489 1026 5611 767 3290 885 4113 1156 4883 1146 5425 892 4414 938 5506 769 3346 677 3673 1184 6542 1009 5088 Construct a scatter plot with this data. Do you observe a relationship between both variables
Answer:
The scatter plot is attached in the image
There exists a positive linear relationship between the two variables i.e sales and advertisements.
Step-by-step explanation:
The scatter plot is attached in the image
There exists a positive linear relationship between the two variables i.e sales and advertisements.
(a[tex]x^{2} x^{2} 3[/tex]
Answer:
[tex]3a {x}^{4} [/tex]
Step-by-step explanation:
remeber that idical laws
[tex] {x}^{a} \times {x}^{b} = {x}^{a + b} [/tex]
Someone help me please!!!
Answer:
Domain: 2<x<7
Range: 1<y<2
Step-by-step explanation:
Range is the y value but domain is the x value
Mark me Brainliest if this works! Thanks!
( 2, 1 ) and ( 7, 2)
Domain - 2 and 7
Range - 1 and 2
I hope you understand...
Mark me as brainliest...
Do u know this question
Answer:
a rectangle
Step-by-step explanation:
because 2 sides are the same the other 2 arent it has four sides with straight angles
Answer:
B.
Step-by-step explanation:
Consider a process that includes careful testing of each manufactured defibrillator. Listed ( below are the numbers of defective defibrillators in 20 successive batches of 10,000. Find the values you would use for the centerline, the upper control limit, and the lower control limit.
20 14 22 27 12 12 18 23 25 19 24 28 21 25 17 19 17 22 15 20
a. p = 0.040000
UCL 0.041 039, LCL = 0.03 8961
b. p 0.002000
UCL= 0.003340, LCL= 0.000660
c. p=0.0020000
UCL = 0, 021200, LCL = 0
d. p 0.040000
UCL = 0.041470, LCL = 0.038530
Ms. Garcia watched 6 commercials
during a 24-minute program. At that rate, how many
commercials would she watch in an hour?
Answer:
15 commercials
Step-by-step explanation:
6 commercials --> 24 minute
x commercials --> 60 minute(1 hour)
x*24 = 6*60
clear x
x = (6*60)/24
x= 15
What is the slope formula?
Answer:
(y2-y1)/(x2-x1)
Step-by-step explanation:
The slope is the change in y over the change in x
(y2-y1)/(x2-x1)
where ( x1,y1) and (x2,y2) are two points on the line
Answer:
O A. [tex]\frac{y2-y1}{x2-x1}[/tex]
Step-by-step explanation:
This is just about how the Slope-Formula works
ok so you get two points off a graph then you use it to plot it in the Slope-Formula like this
for example imma go with (-2, 5) and (3, 7)
I need to subtract 7 - 5 / 3 - -2. so...
m = slope
m = [tex]\frac{y2-y1}{x2-x1}[/tex]
m = [tex]\frac{7-5}{3--2}[/tex] Only add the denominators when there's 2 - signs together
m = [tex]\frac{2}{5}[/tex]
Find the value of x.
1680
x = [? ]°
The value of x is 84 degrees.
What is tangent to a circle?
The tangent line to a circle at a given point is the straight line that just touches the circle at the point.
A tangent to a circle is perpendicular to the radius at the point of tangency.
According to the question
we have to find the value of x.
Let us assume that a circle have a center at O. And Mark the end of the given chord P and Q.
Connect OP and OQ.
here,
OP = OQ
⇒∠OQP = ∠QPO
Now in triangle POQ, we have
⇒∠QOP + 2∠ OPQ = 180
⇒168 +2∠OPQ =180
⇒2∠OPQ = 12
⇒∠OPQ =6 degrees.
As we know that, tangent to a circle is perpendicular to the radius at the point of tangency.
⇒ x + ∠QOP = 90
⇒ x + 6 = 90
⇒ x = 90-6 = 84 degrees.
Hence, value of x is 84 degrees.
Learn more about the tangent to the angle here:
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if I buy a dozen cupcakes for $16.80, How much will 16 cupcakes cost.
Answer:
i aint gon lie evolution and natural selection?
Step-by-step explanation:
Only answer if you're very good at Math.
Given f(x) = x + 1 and g(x) = x^2, what is
( g o f) (x)?
A: ( g o f) (x) = x^2 + 1
B: ( g o f) (x) = ( x + 1)^2
C: ( g o f) (x) = x^2 + x + 1
D: ( g o f) (x) = x^2 ( x + 1)
Answer:
The answer is B: ( g o f) (x) = ( x + 1)^2
Explanation:
⟹ (g ∘ f) (x) = g [f (x)]
Replace x in g(x) = x^2 with x+1
= ( x + 1 ) ^2
Some help with this pleaseee!
Answer:
g(x) = |x| + 7
Step-by-step explanation:
Adding the constant +7 on the end of the equation means a translation 7 units up.
An angle measuring 60 degrees is measured as 62 degrees. What is the percentage error correct to 3 significant figures?
35.5%
3.33%
3.23%
37.2%
Answer: 3.33% (choice B)
===================================================
Work Shown:
A = true value = 60
B = estimated or measured value = 62
C = percent error
C = ( |A-B|/A ) * 100%
C = ( |60-62|/60 ) * 100%
C = (2/60)*100%
C = 0.0333*100%
C = 3.33%
The result is approximate.
How is 10+10 the same as 11+11?
Answer:
I only remember the funny thing my dad told me
210
What is the arc length when
=
and the radius is 6 cm?
Answer:
ans : option 2nd
Step-by-step explanation:
total angle substand perimeter of circle so,
so solve by using unitary methods
A man bought a car for $8200 and sold it for 80% of the price two years later. How much did he lose?
Answer:
I don't know for sure, but I'm pretty sure its 1,640.
Step-by-step explanation:
80% of 8,200 is 6560, and then do 8,200- 6,560, you get 1,640.
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According to question, The price at which it was sold is equal to :
[tex]80 \% \: \: of \: \: 8200[/tex][tex] \dfrac{80}{100} \times 8200[/tex][tex]80 \times 82[/tex][tex]6560[/tex]The car was sold at $ 6560
Now, loss is equal to :
[tex]8200 - 6560[/tex][tex] \$ \: 1640[/tex]please answer this thank you
Answer:
diameter [d]=15cm
radius [r]=7.5cm
slant height be l
and
height be h.
lateral surface area of cone =
πrl=477cm²
l=477/(3.1416*7.5)
l=20.244
now
h=[tex]\sqrt{20.2²-(7.5/2)²}=20cm[/tex]
height=20cm.
LSA of cone = πrl = 477cm²
L = 477/(3.1416 × 7.5)
L = 20.244
Height (h) = √{20.2²-(7.5/2)²}
h = 20cm
see the picture please!!
Answer:
the first one its true
y of A greater than the y of B
Write the number 0.000 378 21 in standard form.
help please
Answer:
3.7821 (SDF)
Step-by-step explanation:
Take the number by 378 21 and place it in the right forms/place marks. Such as ones and tens place ect. Then there is your answer.
School is almost over pls help
Answer:
3. pollution
4. the land becomes fertile